Following is a question from a past paper

"Write the equation of Damped Harmonic Oscillator and discuss all three conditions of damping."

I cannot find the three conditions of damping in the recomended books. The genral equation of damped oscillator has been explained in the recomended books.
After some net surfing I dug out the 3 conditions of damping with little explanation, but without derivation.

Now I want to ask, if this question is asked again then do i need detailed derivation of all 3 conditions or derivation of genral equation and some explanation of 3 conditions will suffice the need?

Dear members please share your view and do mention some source from where I can find derivation of 3 conditions of damping (if it is required).